Co-evolution is a fundamental component of the theory of evolution and is essential for understanding the relationships between species in complex ecological networks. A wide range of co-evolution-inspired computational methods has been designed to predict molecular interactions, but it is only recently that important advances have been made. Breakthroughs in the handling of phylogenetic information and in disentangling indirect relationships have resulted in an improved capacity to predict interactions between proteins and contacts between different protein residues. Here, we review the main co-evolution-based computational approaches, their theoretical basis, potential applications and foreseeable developments.